Quantum-Gravitational Backreaction in the BTZ Background from Curved Momentum Space
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| Format: | Preprint |
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2025
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| _version_ | 1866909033946939392 |
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| author | Nandi, Partha Roy, Mainak Horoto, Langa Scholtz, Frederik G. Chakraborty, Biswajit |
| author_facet | Nandi, Partha Roy, Mainak Horoto, Langa Scholtz, Frederik G. Chakraborty, Biswajit |
| contents | We explore how quantum properties of spacetime, specifically the curvature of momentum space, can backreact on classical gravity within a tractable semiclassical (2+1)-dimensional framework with a negative cosmological constant. Motivated by quantum-gravity scenarios, we investigate how Planck-scale modifications of particle kinematics influence both dynamics and gravitational solutions. Starting from a first-order action, we derive an effective configuration-space description and show that particle trajectories remain geodesic, preserving the weak equivalence principle despite the underlying deformation. Coupling this modified matter sector to Einstein gravity, we obtain a deformed BTZ black hole solution. Remarkably, the local geometric structure and thermodynamic relations retain their standard form, while all quantum-gravity effects are encoded in a nonlinear mapping between the microscopic mass parameter and the ADM mass. This induces a renormalization of the horizon radius and thermodynamic quantities without altering their functional dependence. As a concrete observable consequence, we compute corrections to the return time of massless probes traveling along null geodesics between the horizon and the AdS3 boundary. Our results demonstrate that Planck-scale kinematic effects can leave controlled and potentially measurable imprints on classical geometry, providing a clear and consistent bridge between quantum-gravity ideas and semiclassical observables. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2509_05713 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Quantum-Gravitational Backreaction in the BTZ Background from Curved Momentum Space Nandi, Partha Roy, Mainak Horoto, Langa Scholtz, Frederik G. Chakraborty, Biswajit General Relativity and Quantum Cosmology High Energy Physics - Theory We explore how quantum properties of spacetime, specifically the curvature of momentum space, can backreact on classical gravity within a tractable semiclassical (2+1)-dimensional framework with a negative cosmological constant. Motivated by quantum-gravity scenarios, we investigate how Planck-scale modifications of particle kinematics influence both dynamics and gravitational solutions. Starting from a first-order action, we derive an effective configuration-space description and show that particle trajectories remain geodesic, preserving the weak equivalence principle despite the underlying deformation. Coupling this modified matter sector to Einstein gravity, we obtain a deformed BTZ black hole solution. Remarkably, the local geometric structure and thermodynamic relations retain their standard form, while all quantum-gravity effects are encoded in a nonlinear mapping between the microscopic mass parameter and the ADM mass. This induces a renormalization of the horizon radius and thermodynamic quantities without altering their functional dependence. As a concrete observable consequence, we compute corrections to the return time of massless probes traveling along null geodesics between the horizon and the AdS3 boundary. Our results demonstrate that Planck-scale kinematic effects can leave controlled and potentially measurable imprints on classical geometry, providing a clear and consistent bridge between quantum-gravity ideas and semiclassical observables. |
| title | Quantum-Gravitational Backreaction in the BTZ Background from Curved Momentum Space |
| topic | General Relativity and Quantum Cosmology High Energy Physics - Theory |
| url | https://arxiv.org/abs/2509.05713 |