USAAAO 2026, I кръг — Задача 8

USAAAO 2026 - First Round · 9 февруари 2026 г.

Problem writers

Problem writers: Srihari (Hari) Balaji, Vincent Bian, Ferdinand, Hagan Hensley, Elizabeth Lee, Joe McCarty, Lucas Pinheiro, Feodor Yevtushenko

Условие

Use the following information for Questions 7 and 8. One of Stephen Hawking’s most famous predictions was the existence of Hawking radiation. Specifically, black holes act like thermal blackbodies and thus must emit blackbody radiation. According to Hawking, a black hole radiates a blackbody spectrum with peak wavelength $\lambda_{max}$ proportional to its Schwarzschild radius $R_s$. Treat the surface of the blackbody as being at the black hole’s event horizon.

Next, interpret the radiated power $P$ from the previous problem as a gradual loss of the black hole’s intrinsic mass-energy $E = Mc^2$. Consider the graph of the black hole’s mass versus time. Which of the following best describes the shape of the resulting graph?

(a) Increasing and concave up

(b) Constant

(c) Decreasing and concave down

(d) Linearly decreasing

(e) Decreasing and concave up

Отговори

Решение

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Оригинал в Архива: usaaao_first_exam_2026.pdf · официални решения: usaaao_first_exam_solutions_2026.pdf