Ten new exact vacuum solutions, including black holes with zero entropy, arise in extended bumblebee gravity because varying the action and imposing the vector VEV constraint do not commute.
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An exact dyonic black hole metric is derived in Lorentz-violating gravity with background Kalb-Ramond field and nonminimal EM coupling; geodesics and extended thermodynamics are analyzed showing parameter-dependent shadows and first-order phase transitions.
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New Exact Vacuum Solutions in Extended Bumblebee Gravity
Ten new exact vacuum solutions, including black holes with zero entropy, arise in extended bumblebee gravity because varying the action and imposing the vector VEV constraint do not commute.
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Dyonic Black Holes in Lorentz-Violating Gravity with a Background Kalb--Ramond Field
An exact dyonic black hole metric is derived in Lorentz-violating gravity with background Kalb-Ramond field and nonminimal EM coupling; geodesics and extended thermodynamics are analyzed showing parameter-dependent shadows and first-order phase transitions.