Effective field equation on m-brane embedded in n-dimensional bulk of Einstein and f(R) gravity

Abstract

We have derived effective gravitational field equations on a lower dimensional hypersurface (known as a brane), placed in a higher dimensional bulk spacetime for both Einstein and $f(\mathcal{R})$ gravity theories. We have started our analysis on $n$-dimensional bulk from which the effective field equations on a $(n-1)$-dimensional brane has been obtained by imposing $Z_2$ symmetry. Subsequently, we have arrived at the effective equations in $(n-2)$-dimensions starting from the effective equations for $(n-1)$ dimensional brane. This analysis has been carried forward and is used to obtain the effective field equations in $(n-m)$-dimensional brane, embedded in a $n$-dimensional bulk. Having obtained the effective field equations in Einstein gravity, we have subsequently generalized the effective field equation in $(n-m)$-dimensional brane which is embedded the $n$-dimensional bulk spacetime endowed with $f(\mathcal{R})$ gravity. We have also presented applications of our results in the context of Einstein and $f(\mathcal{R})$ gravity. In both the cases we have discussed vacuum static spherically symmetric solutions as well as solutions in cosmological context. Implications are also discussed.

v2, Revised, Accepted in EPJC, 35 pages, no figures

References in corpus (10)

• Unified cosmic history in modified gravity: from F(R) theory to Lorentz non-invariant models
• Surface Casimir densities and induced cosmological constant in higher dimensional braneworlds
• Spherically symmetric brane spacetime with bulk $f(\mathcal{R})$ gravity
• Living on the edge in a spacetime with multiple warping
• Braneworlds in six dimensions: new models with bulk scalars
• Chiral fermions in a spacetime with multiple warping
• Bulk Higgs and Gauge fields in a multiply warped braneworld model
• Generalized Modified Gravity in Large Extra Dimensions
• Schwarzschild Solution on the Brane
• Matter in the Bulk and its Consequences on the Brane: A Possible Source of Dark Energy

Cited by in corpus (39)

• Strong gravitational lensing --- A probe for extra dimensions and Kalb-Ramond field
• Finite-time Cosmological Singularities and the Possible Fate of the Universe
• Inflation driven by Einstein-Gauss-Bonnet gravity
• Solving higher curvature gravity theories
• Signatures of extra dimensions in gravitational waves from black hole quasi-normal modes
• Shadow of a Charged Rotating Black Hole in $f(R)$ Gravity
• Fate of Strong Cosmic Censorship Conjecture in Presence of Higher Spacetime Dimensions
• Tidal Love Numbers of Black Holes and Neutron Stars in the Presence of Higher Dimensions: Implications of GW170817
• Spherically symmetric brane in a bulk of f(R) and Gauss-Bonnet Gravity
• Hunting extra dimensions in the shadow of Sgr A*
• Horndeski theories confront the Gravity Probe B experiment
• Excavating black hole continuum spectrum: Possible signatures of scalar hairs and of higher dimensions
• Perturbed thermodynamics and thermodynamic geometry of a static black hole in $f(R)$ gravity
• Decoding signatures of extra dimensions and estimating spin of quasars from the continuum spectrum
• Bouncing cosmology from warped extra dimensional scenario
• Looking for extra dimensions in the observed quasi-periodic oscillations of black holes
• Solutions on a brane in a bulk spacetime with Kalb-Ramond field
• Signatures of Einstein-Maxwell dilaton-axion gravity from the observed jet power and the radiative efficiency
• (Compactified) black branes in four dimensional f(R)-gravity
• Black hole shadow and chaos bound violation in $f(T)$ teleparallel gravity
• Gravity stabilizes itself
• Does black hole continuum spectrum signal f(R) gravity in higher dimensions?
• Cloud of strings in f(R) gravity
• (Anti)evaporation of Dyonic Black Holes in string-inspired dilaton $f(R)$-gravity
• Fermion localization in higher curvature and scalar-tensor theories of gravity
• Kinematics of Radion field: A possible source of dark matter
• Evaporation and anti-evaporation instability of a Schwarzschild-de Sitter braneworld: the case of five-dimensional F(R) gravity
• Linearization of a warped $f(R)$ theory in the higher-order frame II: the equation of motion approach
• Black branes in four-dimensional conformal equivalent theories
• Radion tunneling in modified theories of gravity
• Non-trivial time crystal-like ground state for gravitational perturbation in quadratic gravity
• Fine Tuning Problem of the Cosmological Constant in a Generalized Randall-Sundrum Model
• Signatures of Einstein-Maxwell dilaton-axion gravity from the observed quasi-periodic oscillations in black holes
• Suppression of Bekenstein-Hawking radiation in $f(T)$-gravity
• Dynamical modelling of disc vertical structure in superthin galaxy `UGC 7321' in braneworld gravity: An MCMC study
• Anisotropic evolution of 4-brane in a 6D generalized Randall-Sundrum model
• Cosmic Acceleration Caused by the Extra-Dimensional Evolution in a Generalized Randall-Sundrum Model
• Softly broken conformal symmetry with higher curvature terms
• Evaporation and Antievaporation instabilities