Uniform density static fluid sphere in Einstein-Gauss-Bonnet gravity and its universality

Abstract

In Newtonian theory, gravity inside a constant density static sphere is independent of spacetime dimension. Interestingly this general result is also carried over to Einsteinian as well as higher order Einstein-Gauss-Bonnet (Lovelock) gravity notwithstanding their nonlinearity. We prove that the necessary and sufficient condition for universality of Schwarzschild interior solution describing a uniform density sphere for all $n\ge 4$ is that its density is constant.

5 pages, title and abstract modified, one author added, considerable improvement in clarity and precision, one reference added, result unchanged. version to agree with the published paper in Phys. Rev. D

References in corpus (4)

• Lovelock Gravity at the Crossroads of Palatini and Metric Formulations
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• Kaluza-Klein black hole with negatively curved extra dimensions in string generated gravity models
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• Compact objects in pure Lovelock theory
• Extra packing of mass of anisotropic interiors induced by MGD
• Limits on stellar structures in Lovelock theories of gravity
• Buchdahl compactness limit and gravitational field energy
• Buchdahl's inequality in five dimensional Gauss-Bonnet gravity
• Charged compact star model in Einstein-Maxwell-Gauss-Bonnet gravity
• Packing extra mass in compact stellar structures: An interplay between Kalb-Ramond field and extra dimensions
• Higher dimensional generalization of Buchdahl-Vaidya-Tikekar model for super compact star
• Maximum Entropy Principle for Self-gravitating Perfect Fluid in Lovelock Gravity
• Gravitational Perfect Fluid Collapse in Gauss-Bonnet Gravity
• Horndeski fermion-boson stars
• Universality of the Buchdahl sphere
• Properties of relativistic star in 5-D Einstein-Gauss-Bonnet gravity
• A possible testbed for warped extra dimension from the angle of Buchdahl's limit
• Dynamical systems approach to stellar modelling in $f(G,B)$ gravity