Analogy between the Schwarzschild solution in a noncommutative gauge theory and the Reissner-Nordström metric

Abstract

We study modifications of the Schwarzschild solution within the noncommutative gauge theory of gravity. In the present analysis, the deformed solutions are obtained by solving the field equations perturbatively, up to the second order in the noncommutativity parameter $\Theta$, for both exterior and interior solutions of the equations of motion for $e_{\mu }^a\left(x\right)$. Remarkably, we find that this new noncommutive solution is analogous to the Reissner-Nordström solution in the ordinary spacetime, in which the square of electric charge is replaced by the square of the noncommutativity parameter, but with opposite sign. This amounts to the noncommutative Schwarzschild radius $r_{NCS}$ becoming larger than the usual radius $r_S=2M$, instead of smaller as it happens to the Reissner-Nordström radius $r_{RN}$, implying that $r_{NCS}>r_S>r_{RN}$. An intuitive interpretation of this result is mentioned.

V2; 15 pages, improved analysis and discussion clarified, references added. To be published in PRD

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Cited by in corpus (8)

• Noncommutative Scalar Quasinormal Modes of the Reissner Nordström Black Hole
• Energy-dependent noncommutative quantum mechanics
• Entanglement Entropy Renormalization for the NC scalar field coupled to classical BTZ geometry
• Black holes in multi-fractional and Lorentz-violating models
• Squeezed coherent states for gravitational well in noncommutative space
• Propagation of spinors on a noncommutative spacetime: equivalence of the formal and the effective approach
• Noncommutative Reissner-Nordström black hole from noncommutative charged scalar field
• Hawking radiation of scalar particles and fermions from squashed Kaluza-Klein black holes based on a generalized uncertainty principle