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Let's consider 5-metrics $$ dS^2=\left[1+\frac{1}{6}(\varkappa c^2\rho_2a-2\Lambda_1)ar^2\right]d{x^0}^2- \left[ 1-\frac{\varkappa c^2\rho_2a+\Lambda_1)}{3}\cdot r^2 a\right]^{-1}dr^2-r^2d\Omega^2-da^2, $$ $$ d\Omega^2=d\theta^2+\sin^2\theta d\varphi^2, $$ where $\varkappa,\rho_2,\Lambda_1=const$. Gravitational force, operating on a trial body, in 4-dimensional space-time $ <M^4_a, ds^2>= <(x^0, r, \theta, \varphi), dS^2 |_ { a=const }>$, is possible to calculate on a formula from [Landau L., Lifshits E. Theory of field. Moscow, 1973. P.327]: $$ f_\alpha=\frac{mc^2}{\displaystyle\sqrt{1-\frac{v^2}{c^2}}}\left\{-\frac{\partial}{\partial x^\alpha}\ln\sqrt{g_{00}}+\sqrt{g_{00}}\left[\frac{\partial}{\partial x^\beta}\left(\frac{g_{0\alpha}}{g_{00}}\right)-\frac{\partial}{\partial x^\alpha}\left(\frac{g_{0\beta}}{g_{00}}\right)\right]\frac{v^\beta}{c}\right\}. $$ We have $$ f_r=-\frac{mc^2}{6\sqrt{1-v^2/c^2}}\frac{\displaystyle\left[\varkappa c^2\rho_2a-2\Lambda_1\right]ar}{\displaystyle\left[1+\frac{1}{6}(\varkappa c^2\rho_2a-2\Lambda_1)ar^2\right]}, \ f_\varphi=f_\theta= 0. $$ In this case, it is obvious that it is possible to find the functions $\Lambda =\Lambda_1a, \rho =\rho_2a^2$ so that $\rho_2>0$, and $f_r$ changes a sign in $a=0$ and $a=2\Lambda_1 / (\varkappa c^2\rho_2) $ in extensive spatial area with radius $r <c\sqrt{6\varkappa\rho_2}/|\Lambda_1|$ (Inequality is received as a condition of positivity of a denominator in a formula for $f_r$ for every $a$.), i.e. the attraction to the center of $r=0$ is replaced by the repulsion from center $r=0$. Transition through $a=0$ changes a sign of ''the cosmological constant'' $\Lambda$, and observable change of gravitation on antigravitation can be regarded as manifestation of the cosmological repulsion. But upon transition through $a=2\Lambda_1 / (\varkappa c^2\rho_2) $ ''the cosmological constant'' keeps a sign, and it means that we have other type of antigravitation. If $r>c\sqrt{6\varkappa \rho_2}/|\Lambda_1|$, then denominator of $f_r$ is remained positive under $$ a>a_+(r)=\frac{1}{\varkappa c^2\rho_2}[\Lambda_1+\sqrt{\Lambda_1^2-(6\varkappa c^2\rho_2/r^2)}] \ {\rm or}\ a<a_-(r)=\frac{1}{\varkappa c^2\rho_2}[\Lambda_1-\sqrt{\Lambda_1^2-(6\varkappa c^2\rho_2/r^2)}]. $$ If $\Lambda_1>0$, then we have $a_+(r)<2\Lambda_1/(\varkappa c^2\rho_2)$. Hence, for every $r>c\sqrt{6\varkappa \rho_2}/\Lambda_1$ when the parameter $a$ is changed in some small interval $(2\Lambda_1/(\varkappa c^2\rho_2)-\varepsilon(r),2\Lambda_1/(\varkappa c^2\rho_2)+\varepsilon(r)),$ the function $f_r$ changes a sign, i.e. the attraction is replaced by the repulsion. Under $\Lambda_1<0$ we have $2\Lambda_1/(\varkappa c^2\rho_2)<a_-(r)$. Hence, for every $r>c\sqrt{6\varkappa \rho_2}/\Lambda_1$ gravitatiomal force $f_r$ changes sign, when the parameter $a$ is changed in the same interval. Thus, when we are moving in 5-dimensional bulk, i.e. when $a$ is changed, the geometry of 4-brane $M^4_a$ is changed so that gravitation (attraction) is replaced with antigravitation (repulsion).

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Let's consider 5-metrics $$ dS^2=\left[1+\frac{1}{6}(\varkappa c^2\rho_2a-2\Lambda_1)ar^2\right]d{x^0}^2- \left[ 1-\frac{\varkappa c^2\rho_2a+\Lambda_1)}{3}\cdot r^2 a\right]^{-1}dr^2-r^2d\Omega^2-da^2, $$ $$ d\Omega^2=d\theta^2+\sin^2\theta d\varphi^2, $$ where $\varkappa,\rho_2,\Lambda_1=const$. Gravitational force, operating on a trial body, in 4-dimensional space-time $ <M^4_a, ds^2>= <(x^0, r, \theta, \varphi), dS^2 |_ { a=const }>$, is possible to calculate on a formula from [Landau L., Lifshits E. Theory of field. Moscow, 1973. P.327]: $$ f_\alpha=\frac{mc^2}{\displaystyle\sqrt{1-\frac{v^2}{c^2}}}\left\{-\frac{\partial}{\partial x^\alpha}\ln\sqrt{g_{00}}+\sqrt{g_{00}}\left[\frac{\partial}{\partial x^\beta}\left(\frac{g_{0\alpha}}{g_{00}}\right)-\frac{\partial}{\partial x^\alpha}\left(\frac{g_{0\beta}}{g_{00}}\right)\right]\frac{v^\beta}{c}\right\}. $$ We have $$ f_r=-\frac{mc^2}{6\sqrt{1-v^2/c^2}}\frac{\displaystyle\left[\varkappa c^2\rho_2a-2\Lambda_1\right]ar}{\displaystyle\left[1+\frac{1}{6}(\varkappa c^2\rho_2a-2\Lambda_1)ar^2\right]}, \ f_\varphi=f_\theta= 0. $$ In this case, it is obvious that it is possible to find the functions $\Lambda =\Lambda_1a, \rho =\rho_2a^2$ so that $\rho_2>0$, and $f_r$ changes a sign in $a=0$ and $a=2\Lambda_1 / (\varkappa c^2\rho_2) $ in extensive spatial area with radius $r <c\sqrt{6\varkappa\rho_2}/|\Lambda_1|$ (Inequality is received as a condition of positivity of a denominator in a formula for $f_r$ for every $a$.), i.e. the attraction to the center of $r=0$ is replaced by the repulsion from center $r=0$. Transition through $a=0$ changes a sign of ''the cosmological constant'' $\Lambda$, and observable change of gravitation on antigravitation can be regarded as manifestation of the cosmological repulsion. But upon transition through $a=2\Lambda_1 / (\varkappa c^2\rho_2) $ ''the cosmological constant'' keeps a sign, and it means that we have other type of antigravitation. If $r>c\sqrt{6\varkappa \rho_2}/|\Lambda_1|$, then denominator of $f_r$ is remained positive under $$ a>a_+(r)=\frac{1}{\varkappa c^2\rho_2}[\Lambda_1+\sqrt{\Lambda_1^2-(6\varkappa c^2\rho_2/r^2)}] \ {\rm or}\ a<a_-(r)=\frac{1}{\varkappa c^2\rho_2}[\Lambda_1-\sqrt{\Lambda_1^2-(6\varkappa c^2\rho_2/r^2)}]. $$ If $\Lambda_1>0$, then we have $a_+(r)<2\Lambda_1/(\varkappa c^2\rho_2)$. Hence, for every $r>c\sqrt{6\varkappa \rho_2}/\Lambda_1$ when the parameter $a$ is changed in some small interval $(2\Lambda_1/(\varkappa c^2\rho_2)-\varepsilon(r),2\Lambda_1/(\varkappa c^2\rho_2)+\varepsilon(r)),$ the function $f_r$ changes a sign, i.e. the attraction is replaced by the repulsion. Under $\Lambda_1<0$ we have $2\Lambda_1/(\varkappa c^2\rho_2)<a_-(r)$. Hence, for every $r>c\sqrt{6\varkappa \rho_2}/\Lambda_1$ gravitatiomal force $f_r$ changes sign, when the parameter $a$ is changed in the same interval. Thus, when we are moving in 5-dimensional bulk, i.e. when $a$ is changed, the geometry of 4-brane $M^4_a$ is changed so that gravitation (attraction) is replaced with antigravitation (repulsion).

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