Abstract
The static isotropic gravitational field equation, governing the geometry and dynamics of stellar structure, is considered in Einstein–Gauss–Bonnet (EGB) gravity. This is a nonlinear Abelian differential equation which generalizes the simpler general relativistic pressure isotropy condition. A gravitational potential decomposition is postulated in order to generate new exact solutions from known solutions. The conditions for a successful integration are examined. Remarkably we generate a new exact solution to the Abelian equation from the well known Schwarzschild interior seed metric. The metric potentials are given in terms of elementary functions. A physical analysis of the model is performed in five and six spacetime dimensions. It is shown that the six-dimensional case is physically more reasonable and is consistent with the conditions restricting the physics of realistic stars.
Highlights
Exploits of the Event Horizon Telescope [1] in detecting the shadow or photon ring of the back hole M87 as well as the success of detecting gravitational waves [2] has cemented the position of general relativity (GR) as a front-runner amongst gravitational field theories
It has recently been shown by Visser [37], and corroborated by Hansraj and Banerjee [38], that gravitational field theories that go by the names trace-free gravity, f (R, T ) theory as well as Rastall theory are geometrically equivalent to the standard Einstein theory
It is well known that the S√chwarzschild interior metric given by Z = 1 + x and y = a x + 1 + b where a and b are integration constants is a necessary solution of the field equations
Summary
A leading contender in the area of modified gravity is Lovelock theory [3,4]. The Lovelock Lagrangian is a natural tensorial generalisation of the Einstein–Hilbert action of GR preserving diffeomorphism invariance, satisfying the Bianchi identities and generating up to second order equations of motion. It is worth noting that the algorithm we develop in this paper has a wide range of applicability in modified theories of gravity It has recently been shown by Visser [37], and corroborated by Hansraj and Banerjee [38], that gravitational field theories that go by the names trace-free gravity (or unimodular gravity), f (R, T ) theory as well as Rastall theory are geometrically equivalent to the standard Einstein theory. This may be observed from the identical statement of the equation of pressure isotropy in all four of these theories. Given that the isotropy equations which relate the gravitational potentials in the metric are identical, we are allowed to conclude that our results apply trivially to the three modified theories mentioned
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
