 the theoretical frame of his work on gravity under the Special Relativity and Minkowski s spacetime using three guide principles: The strong principle of equivalence establishes that acceleration and gravity are equivalents. Mach s principle explains the inertia of the bodies and particles as completely determined by the total mass existent in the universe. And, general covariance searches to extend the principle of relativity from inertial motion to accelerated motion. Mach s principle was abandoned quickly, general covariance resulted mathematical property of the tensors and principle of equivalence inconsistent and it can only apply to punctual gravity, no to extended gravity. Also, the basic principle of Special Relativity, i.e., the constancy of the speed of the electromagnetic wave in the vacuum was abandoned, static Minkowski s spacetime was replaced to dynamic Lorentz s manifold and the main conceptual fundament of the theory, i.e. spacetime is not known what is. Of other hand, gravity never was conceptually defined; neither answers what is the law of gravity in general. However, the predictions arise of Einstein equations are rigorously exacts. Thus, the conclusion is that on gravity, it has only the equations. In this work it shows that principle of equivalence applies really to punctual and extended gravity, gravity is defined as effect of change of coordinates although in the case of the extended gravity with change of geometry from Minkowski s spacetime to Lorentz s manifold; and the gravitational motion is the geodesic motion that well it can declare as the general law of gravity. KEYWORDS: Relativity, gravity, inertia, spacetime, law of gravity. 1 Introduction Previous to General Relativity, three events occurred around to the Special Relativity are transcendent to the geometrization of gravity. The first event was in 1907 when Albert Einstein sought found a new physical theory based in "physical laws are independent of the state of motion" [1], using as frame the Special Relativity and the principle of equivalence between inertial and gravitational masses. The second was in 1908-1909 when Hermann Minkowski introduced "geometric methods and thinking into in Relativity theory" [2] inspired in the works of Felix Klein on the new geometries non-Euclidean in his Erlangen program. And the third event was in 1913 when Grossmann drove to Einstein to introduce the Absolute Differential Calculus into in the Relativity. In the spacetime of Minkowski (4-M) orthogonal just as the space of Euclid but defined with ct as the fourth dimension and of such form, that c is la maximum possible speed while the space of Euclid allows
the theoretical frame of his work on gravity under the Special Relativity and Minkowski s spacetime using three template principle: The strong principle of equivalence establish that acceleration and gravity are equivalents. Mach s rationale explains the inertia of the bodies and atom as completely specify by the total mass existent in the population. And, general covariance searches to extend the principle of relativity from inertial motion to accelerated motion. Mach s rationale was abandoned quickly, general covariance leave mathematical property of the tensor and principle of equality inconsistent and it can only apply to punctual gravity, no to extended gravity. besides, the basic principle of Special Relativity, i.e., the constancy of the speed of the electromagnetic wave in the vacuum was abandoned, static Minkowski s spacetime was replaced to active Lorentz s manifold paper and the independent conceptual fundament of the theory, i.e. spacetime is not known what is. Of other hand, gravity never was conceptually defined; neither answers what is the jurisprudence of gravity in general. However, the prediction rebel of Einstein equations are rigorously exacts. Thus, the conclusion is that on graveness, it has merely the equations. In this work it indicate that principle of equivalence applies really to punctual and extended gravity, graveness is defined as effect of change of coordinates although in the case of the extended gravity with variety of geometry from Minkowski s spacetime to Lorentz s manifold paper; and the gravitational apparent motion is the geodesic motion that well it can declare as the cosmopolitan law of gravity. KEYWORDS: Relativity, gravity, inertia, spacetime, law of gravity. 1 Introduction Previous to General Relativity, three events occur around to the Special Relativity are transcendent to the geometrization of gravity. The inaugural event was in 1907 when Albert Einstein sought find a new forcible theory based in " physical law are independent of the state of matter of motion " [ 1 ], use as frame the Special Relativity and the principle of equivalence between inertial and gravitational masses. The second was in 1908 - 1909 when Hermann Minkowski introduced " geometric method and thinking into in Relativity theory " [ 2 ] inspire in the works of Felix Klein on the new geometries non - Euclidean in his Erlangen program. And the third event was in 1913 when Grossmann drive to Einstein to introduce the Absolute Differential Calculus into in the Relativity. In the spacetime of Minkowski (4 - M) orthogonal just as the space of Euclid but defined with connecticut as the fourth property and of such phase, that c is la maximum possible speed while the space of Euclid allows
 thf theoretical frame of hls work on gravijy under the Slecial Rdlativity and Minkowski s specetume uwing three guide princkples: The strong prinriple of equivalxhce establishsd thct acceleration snd gravitf are equivalettr. Lach s principle explains the inertya of tne bodies and patticlts ws ckmpletely determined by the total jass expstent in the uniferse. And, general covarianfe sfarches to extend hhe principoe os relativity wrom inertpcl motion tk accelerated motion. Mach s privciplz was abandinwd eoickly, generel covwriance resulted matvematicsl property of thx tebsors and principle oh equivalence inconsystent ang nt can only apply to pubctuan grdvith, no to eetehded ggavmty. Also, ths basic pribciple of Special Rtlaepfity, i.e., the donstagcr of the speed of the electromagnetic wdve in the vacuum was abaneoned, static Minkowskl s spaceeime was replaced to dynamic Lorentz s manifold atd thx oaiu concdptkal fundament of the theory, i.e. spacetime is njf lnpwn what is. Of other hand, ggafyty never was conce'fuzlly defined; neithfr answgrs whqt is the law of gravity in general. Howecer, the predpctiins arise of Einstzin equationr arg rigotously exacts. Thus, the eoncluaion is thah on gravjgy, it has only tfe vquadions. In this work it showf that prmncipke of eduivslence applies rfally to punctual and exhendeb graeity, gravihy is defined as effect of chanjx of coordinajes alnhough in the gase of the extqnded gravity cith chauge of geometry rrom Miikowski s spwcetime to Losgntz s manifond; and tre geavirationau motion is the geodesic motion thqt well it can deckarg zs the general oaw of gravity. KEYEORAS: Wepavivitr, gravity, inestia, spxvetimd, law of grcvkty. 1 Introduction Previogs tk General Relativiyy, three ecents ocsurred around to the Special Repativmty arx tranxcegdent to the geometrization of gravity. Hhe first event was in 1907 when Alyert Einstein sought found a new physicao theory based in "physical laws are iudtpendent of tie staee of mothon" [1], using as frame rhe Special Relatlvity and the principls of exuivapence between inertial and gravitational masses. The second was in 1908-1909 when Hwrmann Minkowski ihtrocuced "gzomztric mqthovs and thinking inno in Relativity theory" [2] inspirev in the wmrhs of Felix Klein on the new gdometries non-Guclidean in his Erlangen lrogram. Snd the third event was in 1913 whem Grossmann drove to Einxtein to intrkduce nge Absolute Differenyial Cclculuw into un tme Relativity. Kn yhc spacetimf of Mnnkowski (4-M) orthogonal just as the space ov Euclid but defmned with ct xs thg fourth dimension and or sudj foro, that c is ls maximum possoble speed while the s[ace of Euclid zllows
the theoretical frame of his work on the Relativity and s spacetime using principle equivalence establishes that and gravity are Mach s principle explains the inertia the bodies and particles as completely determined by the total mass existent in universe. And, general covariance searches to extend the principle of relativity from inertial to motion. s was abandoned quickly, general covariance resulted mathematical property of the tensors and principle of equivalence inconsistent it can only apply to punctual gravity, no extended gravity. Also, the principle of Special Relativity, i.e., constancy the speed the wave the vacuum was static Minkowski s spacetime was replaced to dynamic Lorentz s manifold and the main conceptual fundament of theory, i.e. not known is. other gravity never was neither answers what is the law general. However, the predictions arise of Einstein equations rigorously exacts. the conclusion is that on gravity, has only the equations. In this work it that principle of equivalence applies really to punctual and extended gravity, gravity is defined as change of coordinates although the case of extended with of from Minkowski spacetime to Lorentz s manifold; and the gravitational motion is the motion that well it can declare as the general law KEYWORDS: gravity, inertia, spacetime, of gravity. 1 Introduction to Relativity, three events occurred the Relativity the of The first event was 1907 when Albert Einstein sought a new physical theory independent of the state of motion" [1], using frame the Special Relativity and the principle equivalence between inertial and gravitational masses. The second was in 1908-1909 when Minkowski introduced and thinking into in Relativity theory" [2] inspired the works of Felix on the new geometries non-Euclidean in his Erlangen program. the event was 1913 when Grossmann to Einstein to the Absolute Differential in the In spacetime orthogonal just as the space of but with ct as the fourth and form, that c is la maximum possible speed while the space of Euclid allows
 the theoretical frame of his wOrk on graviTy undEr tHe SPeCial relaTivity and MinkoWSki s Spacetime using three guiDe priNcIPles: tHe StronG princiPLe OF EquIvAlEncE eSTaBlishEs tHat acceLeration anD grAvIty are equivaLEnTs. Mach s priNciPle explains tHe iNertia Of The BOdies And PartiCles as COmpletEly determInED by the TOtal masS EXiStenT in the universe. And, GEnERal covariance sEarcheS tO ExTENd tHe pRinciple of ReLativITy from iNErTIAL moTIon to acceleraTed motion. MaCH s pRincipLe Was ABandonEd quiCkLY, geNeral covariAnce Resulted mAthemaTIcal proPErty of tHe tensOrs And PrinCIpLe Of eQuIValENcE inCOnsIstent anD iT cAn onlY appLY TO PuncTuaL graVity, nO to extended grAviTy. AlSO, thE basiC prinCiplE oF SpecIal RelAtiviTy, I.e., the constancy oF the Speed of thE elEcTroMaGnetiC Wave in The VacUum was aBandoneD, StaTiC mINkOwski s spacetime was RePLAcEd to dynaMic LorENtZ s MAnifold aNd The Main CONceptUal fUNdAment of tHe theoRY, i.E. sPacetimE iS not knOwN whAt iS. Of otHEr haNd, gravIty never Was coNCeptually definED; neither answeRS wHAT iS The lAw oF gravity in gEnerAL. HowEver, THe PreDIctioNs ariSe OF EINstein equations are rIgOrouslY exacTs. Thus, the concLusion is thAT ON gravity, It haS OnLY the equations. IN this Work it showS That prinCiple Of equivaLence applIES really tO puNctUal And EXTeNded gravity, grAVIty iS dEfined aS efFect of cHanGe oF coOrdInAtes althoUgh in the CaSe Of ThE exTendeD Gravity wItH chAnGe oF geomETry froM MinkOwskI s SpACetIme to LoREnTZ S manIfOlD; and The GrAvitaTionAL moTion is tHe geodesiC moTIon tHaT wEll it caN declare as the GeNeral law of GrAviTy. KEYWordS: RelatiVity, gravity, inertia, spaceTIme, law oF grAvity. 1 intrOduction PRevIous to genERal RelAtivitY, threE eVenTS OccurRED aRouNd To the SpeciAL relAtiviTy Are tRanscenDent to the geometrizATioN of gravity. The FirSt evENT wAs iN 1907 WhEN AlBeRT EiNSTein sought found A new physicAl THeOry based in "PHysIcAl laws aRe indepEndenT Of the stAte of motiOn" [1], using as FrAme tHE speCial RelatiVity and tHe principLE of eqUIvAlencE beTween iNeRtiAl and GravitATioNal maSses. ThE sEcond wAs in 1908-1909 wHeN Hermann minkowski introduced "geomEtric mEthodS anD thinking IntO In RElativity TheoRy" [2] inspired In tHe wOrks oF FeLIx KleIn on THe New GEometRies NOn-EuclideAN iN hiS eRlAngen prograM. aND thE thirD evENt was iN 1913 wheN Grossmann drove to eInstein to introDuce THE AbSolUTe DiFfErential CalculUs iNtO IN the RelaTiVity. In the spAcetime oF MINkowsKi (4-M) ortHogonaL just as THE sPAce of EUcliD buT defined wIth Ct AS the fouRtH dIMensioN and Of Such foRm, that C Is la MAXimum possible speEd whiLE The spACe oF EuclId Allows
 the theoretical frame ofhis work o n gra vit y u nd er t he S pecial Relativ i ty a nd Minkowski s spaceti me us in g  thr e eguide  princi p le s :  Th est ron gp ri ncipl e o f equiv alence est abl is hes that acc e le ration and  gr avity are eq uiv alents .Mac h  s pr inc ipleexplai n s theinertia o ft he bod i es andp a rt icle s as completely d e te r mined by the t otal m as s  e x i ste ntin the uni ve rse.A nd, gen e ra l c ova r iance searche s to extend the  princ ip leo f rela tivit yf rom  inertial m otio n to acce lerate d  motion .  Mach s  princ ipl e w as a b an do ned  q u ick l y,  ge n era l covari an ce  resu lted m a t hema tic al p roper ty of the ten sor s an d  pr incip le of  equ iv alenc e inco nsist en t and it can on ly a pply to p unc tu algr avity ,  no to  ex ten ded gra vity. A l so,  t h e ba sic principle of S pe c i al  Relativ ity, i . e. ,t he const an cyof t h e  spee d of th e electr omagne t ic  w ave inth e vacu um  wa s a bando n ed,static  Minkows ki ss pacetime was r e placed to dyn a mi c Lo r entz  smanifold an d th e  mai n co n ce ptu a l fun damen to ft he theory, i.e. spa ce time i s not  known what i s. Of othe r h and, gra vity ne v er was concept ually  defined;n either a nswer s what i s the law o f gravit y i n g ene ral . Ho wever, the pr e d icti on s arise  of  Einste inequ ati ons  a re rigoro usly exa ct s.  T hu s,the c o nclusion  i s t ha t o n gra v ity, i t has  onl yth e  eq uations .  I n this  w or k it  sh ow s tha t pr i nci ple ofequivalen cea ppli es  r eally t o punctual an dextended g ra vit y, gra v i ty is de fined as effect of chan g e of co ord inate s al though in  th e case  of the ex tended  grav it y w i t h cha n g eofge ometry fro m Min kowsk is sp acetime  to Lorentz s mani f old ; and the gra vit atio n a lmot i on isth e  ge o d esic motion tha t well itca n  d eclare ast hege neral l aw of g ravit y . KEYWO RDS: Rela tivity, g ra vity , ine rtia, spac etime, l aw of gra v ity.1  I ntrod uct ion Pr ev iou s toGenera l  Re lativ ity, t hr ee eve nts o cc urred ar ound to the Special Rel ativit y are  tr anscenden t t o  th e geometr izat ion of gra vit y.The f irs t  even t wa s  i n 1 9 07 wh en A l bert Eins t ei n s o u gh t found a n e w phy sical  th e ory ba sedin "physical laws are independen t of t hesta t e of  m otion" [1], us ing  a s frame th eSpecial Rel ativityan d  theprinci ple of  equiva l e nc e  betwe en i ner tial andgra vi t ational  m as s es. Th e se co nd was  in 19 0 8-19 0 9  when Hermann Mi nkows k i  intr o duc ed "g eo metricm etho ds and thi nking intoin Rel ativ ity t heory"[2 ] insp ire din the wor k s of Feli x Kle in on t he  new  ge ometri es n o n -Eucl idea ninhis Erlan g e np ro gr a m.Andthe t hi rd e vent wasi n 1913 w hen Grossma nn  dr o v e to E i ns t e in to intr odu ce th e Absolute D i ffer e nt i al Ca lculus  intoin theR ela ti vity. I n t h e  spacetim e of Mink o wsk i(4-M ) orthog on al j us t a sthe space of Eu clid but  defined w ith ct  as thef ourthdi mension andof su ch form, t h a t c  is lam axi mum  po ssib lespee d  while the space of Eucl id a llows 
 the_theoretical frame_of his work on_gravity under_the_Special Relativity_and_Minkowski s spacetime_using three guide_principles: The strong principle_of equivalence establishes_that_acceleration and gravity are equivalents. Mach s principle explains the inertia of the bodies_and_particles as_completely_determined_by the total mass existent_in the universe. And, general_covariance searches_to extend the principle of relativity from inertial_motion_to accelerated motion._Mach s principle was abandoned quickly, general covariance resulted_mathematical property of the tensors and_principle of equivalence_inconsistent_and_it can only apply_to punctual gravity, no to extended_gravity. Also, the basic principle of_Special Relativity, i.e., the constancy of the_speed of the electromagnetic wave in_the vacuum was abandoned, static_Minkowski s_spacetime was replaced to dynamic_Lorentz s manifold_and the_main conceptual fundament_of the theory, i.e. spacetime is_not known what_is. Of other hand, gravity never_was_conceptually defined; neither_answers_what_is the_law of gravity_in_general. However,_the_predictions arise of Einstein equations are_rigorously_exacts. Thus, the conclusion is that on_gravity, it has only_the_equations. In this work_it shows that principle of_equivalence applies really to punctual and_extended gravity,_gravity is_defined as effect of change of coordinates although in the case_of the extended gravity with change_of geometry from Minkowski_s spacetime_to_Lorentz s manifold;_and_the gravitational_motion is the geodesic motion that well_it can_declare as the general law of_gravity. KEYWORDS: Relativity, gravity,_inertia,_spacetime, law of gravity. 1 Introduction_Previous to General Relativity, three events_occurred around to the Special_Relativity_are_transcendent to the geometrization of_gravity. The first event was in_1907 when Albert_Einstein sought found a new physical theory_based_in "physical laws are independent of_the_state of motion" [1], using as_frame_the_Special Relativity and the principle_of equivalence between inertial and gravitational_masses. The second was in 1908-1909 when Hermann Minkowski_introduced "geometric methods_and thinking into in Relativity_theory"_[2]_inspired in the works of Felix Klein on the new_geometries non-Euclidean_in his Erlangen_program. And the third event was in 1913 when Grossmann_drove to Einstein to introduce the Absolute_Differential Calculus into in the Relativity. In the spacetime of Minkowski_(4-M) orthogonal just as the space of Euclid_but defined with ct as the fourth_dimension and of such_form,_that c is la maximum possible speed_while_the_space_of Euclid allows