Abstract
We explore a connection between generalized uncertainty principle (GUP) and modified Hořava–Lifshitz (HL) gravity. The GUP density function may be replaced by the cutoff function for the renormalization group of modified Hořava–Lifshitz gravity. We find the GUP-corrected graviton propagators and compare these with tensor propagators in the HL gravity. Two are qualitatively similar, but the p5-term arisen from Cotton tensor is missed in the GUP-corrected graviton propagator.
Highlights
Horava has proposed a renormalizable theory of gravity at a Lifshitz point [1], which may be regarded as a UV complete candidate for general relativity
The HL gravity theory has been intensively investigated in [2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27], its cosmological applications in [28, 29], and its black hole solutions in [30, 31, 32]. It seems that the generalized uncertainty principle (GUP) effect on the Schwarzschild black hole is related to black holes in the deformed Horava-Lifshitz gravity [33]
We could not confirm a solid connection between the GUP and the black hole of modified Horava-Lifshitz gravity, we have obtained partial connections between them
Summary
Horava has proposed a renormalizable theory of gravity at a Lifshitz point [1], which may be regarded as a UV complete candidate for general relativity. The HL gravity theory has been intensively investigated in [2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27], its cosmological applications in [28, 29], and its black hole solutions in [30, 31, 32]. But the p5-term arisen from Cotton tensor is missed in the GUP-corrected graviton propagator
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