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Nonlocal Massive Gravity from Einstein Gravity.

Pablo Bueno1, Pablo A Cano1, Robie A Hennigar1

  • 1Departament de Física Quàntica i Astrofísica, Institut de Ciències del Cosmos Universitat de Barcelona, Martí i Franquès 1, E-08028 Barcelona, Spain.

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We introduce nonlocal massive gravity (NLMG), a new theory derived from Einstein gravity on a modified brane. This theory resolves short-distance gravitational behavior, potentially allowing for asymptotically flat black hole solutions.

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Area of Science:

  • Theoretical physics
  • Gravitational theories
  • Higher-dimensional gravity

Background:

  • Einstein gravity is the standard theory of gravity.
  • Massive gravity theories aim to explain gravitational phenomena with massive gravitons.
  • Higher-derivative corrections are often introduced to modify gravitational theories.

Purpose of the Study:

  • To construct a three-dimensional nonlocal theory of massive gravity (NLMG).
  • To analyze the properties of NLMG, including its spectrum and gravitational potential.
  • To investigate the possibility of asymptotically flat black hole solutions within NLMG.

Main Methods:

  • Top-down construction of NLMG from Einstein gravity on a modified brane.
  • Derivation of an analytic formula for the quadratic action of NLMG.
  • Analysis of the linearized spectrum and Newtonian potential.
  • Incorporation of brane-world holography principles.

Main Results:

  • NLMG is constructed, involving an infinite series of higher-derivative corrections.
  • The linearized spectrum of NLMG consists of an infinite tower of positive-energy massive spin-2 modes.
  • The Newtonian potential in NLMG exhibits a 1/r behavior at short distances, unlike truncated theories.

Conclusions:

  • The nonlocal massive gravity theory offers a novel framework for massive gravity.
  • The 1/r behavior of the Newtonian potential suggests a resolution to short-distance issues.
  • NLMG may support the existence of asymptotically flat black hole solutions.