Nonlinear perturbations of Reissner-Nordström black holes
We develop a nonlinear perturbation theory of Reissner-Nordstr\"om black holes. We show that, at each perturbation level, Einstein-Maxwell equations can be reduced to four inhomogeneous wave equations, two for polar and two for axial sector. Gravitational part of these equations is similar to Regge-Wheeler and Zerilli equations with source and additional coupling to the electromagnetic sector. We construct solutions to the inhomogeneous part of wave equations in terms of sources for Einstein-Maxwell equations. We discuss $\ell=0$ and $ \ell=1$ cases separately.
Towards a theory of nonlinear gravitational waves: A systematic approach to nonlinear gravitational perturbations in the vacuum
We present a systematic and robust approach to nonlinear gravitational perturbations of vacuum spacetimes. This approach provides a basis for a theory of nonlinear gravitational waves. In particular, we show that the system of perturbative Einstein equations reduces at each perturbation order to two (for each gravitational mode in 3 + 1 dimensions on which our study is focused) scalar wave equations, and then we show how the metric perturbations can be explicitly obtained, once the solutions to these scalar wave equations are known. These results show that the concept of polarization of a gravitational wave does make sense also beyond the linear approximation.
Habituation Protocols Improve Behavioral and Physiological Responses of Beef Cattle Exposed to Students in an Animal Handling Class
Simple Summary Students in agricultural programs have the opportunity to interact with animals during different teaching activities. However, students’ interactions with livestock may be distressing to the animals and can affect the students’ and animals’ safety. We investigate whether two human-animal habituation strategies, one with positive tactile stimulation and one without, would improve behavioral and physiological responses of beef heifers during a livestock handling class. Overall, heifers that received a habituation treatment had more positive behavior responses, and decreased physiological stress responses in comparison to heifers that were not exposed to habituation. Furthermore, the heifers exposed to the habituation with a positive tactile stimulation had the greatest improvements in behavior in comparison to control and non-stimulated heifers, exhibiting more positive behaviors when interacting with humans. Strategies to habituate cattle to human interaction with positive stimulation aligned with training humans that handle and interact with cattle on best practices and cattle behavior can improve behavior, reduce stress-related physiological responses and enhance safety for both humans and animals. Abstract Our objective was to determine the impact of different habituation protocols on beef cattle behavior, physiology, and temperament in response to human handling. Beef heifers were exposed to three habituation strategies: (1) tactile stimulation (brushing) in the working chute for seven consecutive days (STI; n = 18); (2) passage through the working chute for seven consecutive days (CHU; n = 19) and; (3) no habituation (CON; n = 19). Individual heifer respiratory rate (RR; n/min), internal vaginal temperature (VAGT; °C), and blood cortisol were measured. Further, behavior parameters were observed to generate a behavior score, and heifer interaction with students and their behavioral responses were recorded. Habituation with STI and CHU resulted in improved numerical behavioral scores compared to CON, and greater (p ≤ 0.05) handling latencies. Vaginal temperature was decreased in STI compared to CHU and CONT (p ≤ 0.05). Cortisol concentration did not differ among treatments, but decreased (p ≤ 0.05) from the start of the experiment to 14 days after treatment initiation. Both habituation protocols showed benefits, but heifers that received the positive tactile stimulation in the chute had the greatest behavior improvements. Furthermore, these heifers responded more calmly during student-animal interactions in class, which is beneficial for the students’ and animals’ safety.